改进CEEMDAN结合新型小波变换的激光雷达去噪算法

doi:10.12305/j.issn.1001-506X.2024.12.14

摘要/Abstract

摘要：

针对激光雷达远距离探测时回波信号背景噪声大问题, 将自适应噪声完备集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise, CEEMDAN)、去趋势波动分析(detrended fluctuation analysis, DFA)和新型小波变换相结合, 提出一种激光雷达去噪算法。首先, 激光雷达回波信号通过CEEMDAN进行分解, 获得多个本征模态函数(intrinsic mode function, IMF)。其次, 引入DFA算法计算各IMF分量与原始回波信号的标度指数, 自适应地将IMF分量划分为信息主导分量和噪声主导分量。再次, 采用新型小波变换对噪声主导分量进行去噪处理。最后, 将信息主导分量和去噪后的噪声主导分量进行信号合并重建。激光雷达仿真信号在-10 dB的去噪结果表明, 与改进的CEEMDAN结合小波软硬阈值相比, 所提算法的均方根误差分别降低了52.13%和96.49%, 信噪比分别提高了3.932 3 dB和3.754 2 dB。实测信号的去噪结果也表明, 所提算法在低信噪比条件下稳健性好且去噪性能更佳。

关键词: 激光雷达, 去噪, 自适应噪声完备集合经验模态分解, 小波阈值函数

Abstract:

In order to solve the problem of high background noise of the return signals in the long-distance detection of lidar, a lidar denoising algorithm is proposed by combining complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), detrended fluctuation analysis (DFA) and novel wavelet transform. Firstly, the lidar return signal is decomposed by CEEMDAN to obtain multiple intrinsic mode function (IMF). Secondly, the DFA algorithm is introduced to calculate the scaling exponent of each IMF component with respect to the original return signal, adaptively divide the IMF components into signal-dominant components and noise-dominant components. Thirdly, the novel wavelet transform is used to denoise the noise-dominant components. Finally, the signal-dominant components are combined with the denoised noise-dominant components for signal reconstruction. The denoising results of the lidar simulation signal at -10 dB show that compared with the improved CEEMDAN combined with wavelet soft and hard thresholds, the root mean square error of the proposed algorithm has decreased by 52.13% and 96.49% respectively, and the signal to noise ratio has increased by 3.932 3 dB and 3.754 2 dB respectively. The denoising results of the measured signal also indicate that the proposed algorithm has good robustness and better denoising performance under low signal to noise ratio conditions.

Key words: lidar, denoising, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), wavelet threshold function

中图分类号:

TP212

冯帅, 曹茹茹, 马愈昭, 丁超. 改进CEEMDAN结合新型小波变换的激光雷达去噪算法[J]. 系统工程与电子技术, 2024, 46(12): 4054-4061.

Shuai FENG, Ruru CAO, Yuzhao MA, Chao DING. Lidar denoising algorithm of improved CEEMDAN combined with novel wavelet change[J]. Systems Engineering and Electronics, 2024, 46(12): 4054-4061.

图/表 11

图1

图2

图3

表1

表2

图4

图5

图6

图7

表3

图8

参考文献 31

1	MAO J D . Noise reduction for lidar returns using local threshold wavelet analysis[J]. Optical and Quantum Electronics, 2012, 43, 59- 68. doi: 10.1007/s11082-011-9503-6
2	XIE C B , ZHAO M , WANG B X . Study of the scanning lidar on the atmospheric detection[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2015, 150, 114- 120. doi: 10.1016/j.jqsrt.2014.08.023
3	JIAO J , YANG G T , WANG J H . Initial multi-parameter detection of atmospheric metal layers by Beijing Na-K lidar[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2017, 188, 46- 51. doi: 10.1016/j.jqsrt.2016.05.018
4	KONG Z , MA T , CHENG Y , et al. A polarization-sensitive imaging lidar for atmospheric remote sensing[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2021, 271, 107747. doi: 10.1016/j.jqsrt.2021.107747
5	VISHNU R , KUMAR Y B , NAIR A K M . An investigation of the elevated aerosol layer using a polarization lidar over a tropical rural site in India[J]. Boundary-Layer Meteorology, 2021, 178 (2): 323- 340. doi: 10.1007/s10546-020-00573-2
6	孙宸, 胡嘉龙, 王昆, 等. 基于小波变换的激光雷达回波信号去噪方法研究[J]. 雷达与对抗, 2022, 42 (4): 20-22, 57.
	SUN C , HU J L , WANG K , et al. Research on a denoising method of lidar echo signals based on wavelet transform[J]. Radar and ECM, 2022, 42 (4): 20-22, 57.
7	邢国军, 刘梧林. 未知环境下激光雷达非平稳数据隔离方法[J]. 现代雷达, 2023, 45 (8): 74- 82.
	XING G J , LIU W L . Nonstationary data isolation method of lidar in unknown environment[J]. Modern Radar, 2023, 45 (8): 74- 82.
8	HU M H , MAO J D , LI J , et al. A novel lidar signal denoising method based on convolutional autoencoding deep learning neural network[J]. Atmosphere, 2021, 12 (11): 1403. doi: 10.3390/atmos12111403
9	TIAN P F , CAO X J , LIANG J N , et al. Improved empirical mode decomposition based denoising method for lidar signals[J]. Optics Communications, 2014, 325, 54- 59. doi: 10.1016/j.optcom.2014.03.083
10	JI S , CAO N W , YANG S P , et al. Inversion of aerosol extinction coefficient by Raman-Mie scattering lidar[J]. Optik, 2020, 203, 164038. doi: 10.1016/j.ijleo.2019.164038
11	ZHANG Y J , WU T , ZHANG X A , et al. Rayleigh lidar signal denoising method combined with WT, EEMD and LOWESS to improve retrieval accuracy[J]. Remote Sensing, 2022, 14 (14): 3270. doi: 10.3390/rs14143270
12	WANG Z Z , DING H B , WANG B X , et al. New denoising method for lidar signal by the WT-VMD joint algorithm[J]. Sensors, 2022, 22 (16): 5978. doi: 10.3390/s22165978
13	QI B L , YANG G H , GUO D B , et al. EMD and VMD-GWO parallel optimization algorithm to overcome lidar ranging limitations[J]. Optics Express, 2021, 29 (2): 2855- 2873. doi: 10.1364/OE.415287
14	WU C , XING W G , XIA L H , et al. Improvement of detection performance on single photon lidar by EMD-based denoising method[J]. Original Research Article, 2019, 181, 760- 767.
15	叶莉华, 李秋生, 卢清. 基于EEMD与多重分形的心电信号特征提取与分类[J]. 信号处理, 2023, 39 (1): 143- 153.
	YE L H , LI Q S , LU Q . Feature extraction and classification of ECG signals based on EEMD and multifractal[J]. Journal of Signal Processing, 2023, 39 (1): 143- 153.
16	CHENG X , MAO J D , LI J , et al. An EEMD-SVD-LWT algorithm for denoising a lidar signal[J]. Measurement, 2020, 168, 108405.
17	GU L , FEI Z W , XU X B . Enhancement method of weak lidar signal based on adaptive variational modal decomposition and wavelet threshold denoising[J]. Infrared Physics & Technology, 2022, 120, 103991.
18	杨瑞, 李维勤, 白清, 等. CEEMDAN-WT降噪提升BOTDA信噪比研究[J]. 电子测量与仪器学报, 2022, 36 (12): 28- 36.
	YANG R , LI W Q , BAI Q , et al. Signal-to-noise ratio improvement for BOTDA using CEEMDAN-WT method[J]. Journal of Electronic Measurement and Instrumentation, 2022, 36 (12): 28- 36.
19	郭晓菲, 欧同庚, 马武刚, 等. 基于CEEMDAN和小波变换的地震信号随机噪声压制新方法[J]. 大地测量与地球动力学, 2022, 42 (11): 1202-1206, 1210.
	GUO X F , OU T G , MA W G , et al. A new random attenuation method of seismic signal Based on CEEMDAN and wavelet transform[J]. Journal of Geodesy and Geodynamics, 2022, 42 (11): 1202-1206, 1210.
20	HU Y J , OUYANG Y , WANG Z L , et al. Vibration signal denoising method based on CEEMDAN and its application in brake disc unbalance detection[J]. Mechanical Systems and Signal Processing, 2022, 187, 109972.
21	马愈昭, 刘逵, 张岩峰, 等. CEEMD结合改进小波阈值的激光雷达信号去噪算法[J]. 系统工程与电子技术, 2023, 45 (1): 93- 100. doi: 10.12305/j.issn.1001-506X.2023.01.12
	MA Y Z , LIU K , ZHANG Y F , et al. Laser radar signal denoising algorithm based on CEEMD combined with improved wavelet threshold[J]. Systems Engineering and Electronics, 2023, 45 (1): 93- 100. doi: 10.12305/j.issn.1001-506X.2023.01.12
22	YANG Y , LI S S , LI C , et al. Research on ultrasonic signal processing algorithm based on CEEMDAN joint wavelet packet thresholding[J]. Measurement, 2021, 201, 111751.
23	HUANG N E , ZHENG S , LONG S R , et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998, 454 (1971): 903- 995. doi: 10.1098/rspa.1998.0193
24	WU Z H , HUANG N E . Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in Adaptive Data Analysis, 2009, 1 (1): 1- 41. doi: 10.1142/S1793536909000047
25	MERT A , AKAN A . Detrended fluctuation thresholding for empirical mode decomposition based denoising[J]. Digital Signal Processing, 2014, 32, 48- 56. doi: 10.1016/j.dsp.2014.06.006
26	MOGHTADERI A , FLANDRIN P , BORGNAT P . Trend filtering via empirical mode decompositions[J]. Computational Statistics and Data Analysis, 2013, 58, 114- 126. doi: 10.1016/j.csda.2011.05.015
27	PENG C K , HAVLIN S , STANLEY H E , et al. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series[J]. Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995, 5 (1): 81- 87.
28	HUANG M, LIU Y Y, YANG G L, et al. An innovation based DFA and EMD method for denoising fiber optic gyroscope drift signal[C]//Proc. of the IEEE 3rd International Conference on Information Science and Control Engineering, 2016: 1262-1266.
29	CUI H M , ZHAO R M , HOU Y L . Improved threshold denoising method based on wavelet transform[J]. Physics Procedia, 2012, 33, 1354- 1359. doi: 10.1016/j.phpro.2012.05.222
30	GONG J . A study on wavelet selection in power signal denoising[J]. IOP Conference Series: Earth and Environmental Science. IOP Publishing, 2021, 675 (1): 012104. doi: 10.1088/1755-1315/675/1/012104
31	XIE B , XIONG Z Q , WANG Z J , et al. Gamma spectrum denoising method based on improved wavelet threshold[J]. Nuclear Engineering and Technology, 2020, 52 (8): 1771- 1776. doi: 10.1016/j.net.2020.01.025

去噪算法	噪声强度/dB
	5		0		-5
	SNR/dB	RMSE(×10^-4)	SNR/dB	RMSE(×10^-4)	SNR/dB	RMSE(×10^-4)
小波硬阈值	19.879 3	0.067 0	17.426 8	0.144 9	16.811 6	0.456 4
小波软阈值	20.091 5	0.059 4	19.760 2	0.173 9	18.804 0	0.140 6
改进小波阈值	25.041 6	0.026 9	24.964 9	0.032 4	23.245 9	0.121 2

项目	参数	取值
发射端	波长/nm	905
	脉冲宽度/ns	100
	单脉冲能量/μJ	20
	脉冲重复频率/kHz	5
接收端	直径/mm	50
	视场角/mrad	1.2
	滤光片带宽/nm	5

去噪算法	噪声强度/dB
	20		5		0		-10
	SNR/dB	RMSE(×10^-4)	SNR/dB	RMSE(×10^-4)	SNR/dB	RMSE(×10^-4)	SNR/dB	RMSE(×10^-4)
算法1	13.360 6	0.098 1	12.536 1	0.750 1	12.386 3	0.564 8	12.958 0	1.620 0
算法2	13.621 5	0.131 2	13.831 7	0.229 8	12.881 0	0.257 1	13.742 7	1.187 1
算法3	19.126 3	0.031 6	17.275 4	0.264 5	17.674 6	0.270 5	17.781 3	0.406 1
算法4	20.660 4	0.022 0	19.935 0	0.081 8	19.093 6	0.160 7	20.756 9	5.113 0
算法5	22.108 3	0.013 1	21.343 3	0.025 9	20.525 5	0.171 1	20.578 8	0.374 8
算法6	23.385 7	0.012 5	24.058 3	0.017 2	24.323 3	0.088 6	24.511 1	0.179 4

[1]	邓志安, 王治国, 王盛鳌, 司伟建. 同步提取变换去噪的雷达信号调制识别方法[J]. 系统工程与电子技术, 2024, 46(10): 3334-3346.
[2]	丛爽, 汪泳钦. 从激光测距到量子纠缠光子对测距[J]. 系统工程与电子技术, 2023, 45(6): 1772-1783.
[3]	曾拥华, 马均瑶, 黄朝燕, 冒智慧, 武婷婷. 联合纯四元数与字典学习的彩色图像去噪方法[J]. 系统工程与电子技术, 2023, 45(2): 373-378.
[4]	马愈昭, 刘逵, 张岩峰, 冯帅, 熊兴隆. CEEMD结合改进小波阈值的激光雷达信号去噪算法[J]. 系统工程与电子技术, 2023, 45(1): 93-100.
[5]	刘紫燕, 马珊珊, 梁静, 朱明成, 袁磊. 注意力机制CNN的毫米波大规模MIMO系统信道估计算法[J]. 系统工程与电子技术, 2022, 44(1): 307-312.
[6]	邵凯, 陈连成, 刘胤. 高移动性Jakes信道的学习与估计[J]. 系统工程与电子技术, 2021, 43(4): 1119-1125.
[7]	刘佩, 贾建, 陈莉, 安影. 基于增强高阶非凸全变分模型的图像去噪算法[J]. 系统工程与电子技术, 2020, 42(3): 557-567.
[8]	马愈昭, 陈楠, 熊兴隆. 基于PCA和相位差校正法的风切变预警算法[J]. 系统工程与电子技术, 2020, 42(1): 52-60.
[9]	王彩云, 赵焕玥, 王佳宁, 李晓飞, 黄盼盼. 快速加权核范数最小化的SAR图像去噪算法[J]. 系统工程与电子技术, 2019, 41(7): 1504-1508.
[10]	熊兴隆, 陈楠, 李永东, 马愈昭, 李猛, 冯帅. 基于卷积神经网络的低空风切变类型识别[J]. 系统工程与电子技术, 2019, 41(4): 772-779.
[11]	王彩云, 胡允侃, 吴淑侠. 基于贝叶斯模型的shearlet域SAR图像去噪方法[J]. 系统工程与电子技术, 2017, 39(6): 1250-1255.
[12]	卢志忠, 周颖, 黄玉. 空间域相关法抗X波段航海雷达同频干扰[J]. 系统工程与电子技术, 2017, 39(4): 758-767.
[13]	胡悦, 仲崇潇, 曹梦宇, 赵旷世. 基于增广拉格朗日乘子的快速高阶全变分图像去噪方法[J]. 系统工程与电子技术, 2017, 39(12): 2831-2839.
[14]	郭晓松, 张东方, 薛海建, 周召发. 基于小波去噪和TLS算法的全姿态寻北[J]. 系统工程与电子技术, 2016, 38(2): 362-367.
[15]	李博, 谢巍. 基于自适应分数阶微积分的图像去噪与增强算法[J]. 系统工程与电子技术, 2016, 38(1): 185-192.